Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar Indian Institute of Technology Madras Examples Example1 Basic wind pressure - calculation A Power house building 25m high is to be designed in Darbhanga city. Compute the basic wind pressure. Basic wind speed in Darbhanga (from appendix A) P. 53 Code V b = 55m/sec An industrial building can be grouped under all general buildings and structures so should be designed for 50 years of design life Risk coefficient from table 1. P. 11 code k 1 = 1 Assuming the terrain is in city industrial area with numerous closely spaced obstructions. It can be grouped under category 3. P.8 code. Since the height of the building is 25m this falls under class B P.11 code. The terrain factor k 2 can be got from table 2 P.12 code. For category 3, class B interpolating between 20m and 30m k 2 = 1.005 The ground is assumed to be plain so the topography factor k 3 is 1 + cs P. 56 code where c = Z / L Since the terrain assumed is plain. Read clause 5.3.3.1 P.12 code k 3 = 1 Design wind speed (V z ) = V b k 1 k 2 k 3 = 55 (1) (1.005) (1) = 55.275 m/sec
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Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Examples
Example1 Basic wind pressure - calculation
A Power house building 25m high is to be designed in Darbhanga
city. Compute the basic wind pressure.
Basic wind speed in Darbhanga (from appendix A)
P. 53 Code Vb = 55m/sec
An industrial building can be grouped under all general buildings and
structures so should be designed for 50 years of design life
Risk coefficient from table 1. P. 11 code
k1 = 1
Assuming the terrain is in city industrial area with numerous closely
spaced obstructions. It can be grouped under category 3. P.8 code. Since the
height of the building is 25m this falls under class B P.11 code. The terrain factor
k2 can be got from table 2 P.12 code. For category 3, class B interpolating
between 20m and 30m
k2 = 1.005
The ground is assumed to be plain so the topography factor k3 is 1 + cs P.
56 code
where c = Z / L
Since the terrain assumed is plain. Read clause 5.3.3.1 P.12 code
k3 = 1
Design wind speed (Vz) = Vb k1 k2 k3
= 55 (1) (1.005) (1)
= 55.275 m/sec
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Design wind pressure = 0.6 VZ2
= 0.6 (55.275)2
= 1833.2 N/m2
Example2
If the above building has to be constructed on a hillock where the
height of the hill is 150m having a slope of 1:3 and the building is proposed
at a height of 100m from the base on hte windward side, find the design
wind
Basic wind speed at Darbhanga = 55m/sec
Risk coefficient k1 =1
Terrain factor k2 = 1.005
To find the topography factor k3 Ref. appendix C. P. 56 code
Z = height of the hill (feather) = 150m
θ = slope in 3 tan-1 (1 / 3) = 18.43o
L = Actual length of upwind slope in the wind direction = 150(3) = 450m
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Le = Effective horizontal length of the hill for θ > 17o Le = Z / 0.3 = 150 / 0.3 =
500m
Values of C for θ = 18.43o (i.e.) > 17o
C = 0.36
Height of the building = 25m
To find x (i.e) the horizontal distance of the building from the crest
measured +ve towards the leeward side and -ve towards the windward side.
k3 = 1 + cs
To get s Fig 14 and 15 are used
x = -150m
x / Le = -150 / 500 = -0.3 H / Le = 25 / 500 = 0.05
Referring to figure 15 hill and ridge for x / Le = -0.3 and H / Le = 0.05 on
the upwind direction
s = 0.58
k3 = 1 + (0.36) (0.58)
k3 = 1.21
Design wind speed Vz = Vb k1 k2 k3
= 55 (1) (1.005) (1.21)
= 66.9 m/sec
Design wind pressure PZ = 0.6 VZ2
= 0.6 (66.9)2
= 2685.4 N/m2
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Example 3:
A memorial building is proposed at Sriperumbudur - Madras on a hill
top. The size of the building is 40m x 80m and height is 10m. The hill is
300m high with a gradiant of 1 in 5. The building is proposed at a distance
of 100m from the crest on the downwind slope. Calculate the design wind
pressure on the building.
Basic wind velocity at madras is 50m/sec Ref. Appendix A. P.53 code
Risk coefficient ks1 = 1.08 for a memorial building of 100 years design life
Terrain factor k2 for category 3 and class C since dimension of building 750m
k2 = 0.82
Topography factor k3
Z = effective height of the hill = 300m
θ = 1 in 5 tan-1 (1/5) = 11.31o
L = Actual length of upward slope in the wind direction = 1500m
Le = effective horizontal length of the hill
For θ = 11.31o Le = L = 1500m
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Topography factor k3 = 1 +cs
where c = 1.2 (Z/L) since θ = 11.31o 3o < θ < 17o
c = 1.2 (300/1500) = 0.24
x is the distance of the building from the crest + on downwind side
- on upward side x = +100m
The non dimensional factors are
x / Le = 100 / 1500 = 0.067; H / Le = 10 / 1500 = 0.0067
s = 1 from fig 15. P.57
k3 = 1 + (0.24) (1);
k3 = 1.24
Design wind speed Vz = Vb k1 k2 k3
= 50 (1.08) (0.82) (1.24)
= 54.91 m/sec
Design wind pressure PZ = 0.6 VZ2
= 0.6 (54.91)2
=1809.1 N/m2
Example 4: Wind pressure on tower on a hill
A microwave tower of 50m height is proposed over a hill top. The
height of the hill is 50m with a gradiant of 1 in 4. The terrain category is 3.
The tower is proposed at coimbatore. Compute the design wind pressure:
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Basic wind speed at CBE is 39m/sec
Risk factor k1 = 1.06
Terrain factor (k2) for category 3 class B - height between 20 and 50
k2 = 1.09 table 2, P.12
Topography factor (k3) Ref. P.56
Z - effective height of the hill = 50m
θ - slope 1 in 4 tan-1 (1/4) = 14.04o
L - Actual length of the upwind slope = 200m
Le - Effective horizontal length of the hill θ = 14.04o < 17
Le = L = 200m
k3 = 1 +cs
θ < 17, c = 1.2 (Z/L) = 1.2 (50/200) = 0.3
x / Le = 0/200 = 0 ; H / Le = 50/200 = 0.25
Ref. Fig.15 s = 0.6; k3 = 1 + (0.3) (0.6)
k3 = 1.18
Design wind speed Vz = Vb k1 k2 k3
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
= 39 (1.06) (1.09) (1.18)
= 53.17 m/sec
Design wind pressure PZ = 0.6 VZ2
= 0.6 (53.17)2
=1696.23 N/m2
Example 5:
If the 50m tower given in previous example is mounted with a hollow
hemispherical dome of 2m diameter weighing 10kN. Compute the forces
and stresses in members of various panels. The elevation of the tower is as
shown below
Data given: Height of the tower = 50m
Base width = 6m
Top width = 2m
No. of panels = 20
Disk size = 2m diameter
Step 1: Wind force - From the previous example
Basic wind speed = 39m/sec
Risk coefficient (k1) = 1.06
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Topography factor (k3) = 1.2
Terrain factor (k2), varies with the height of the tower Ref, P.12 Table 2 code
The design wind pressures at different heights are computed as
PZ = 0.6 VZ2
= 0.6 (39 x 1.06 x 1.2 x k2)2
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
=1476.6 k22 N/m2
The values of k2 at different height is chosen from Table 2
Step2: Basic assumptions:
1. Self weight of the members are equally distributed to the two joints
connected by the members
2. No load is applied at the middle of the k-braced joint but allocated to column
joint
3 Dead and wind loads are increased by 15% for each joints to account for
Gussets, bolts and nuts
4. Secondary members are assumed to be provided in the panel where batter
starts (below the waist level in our case panels 16 to 20. So an additional load of
10% is accounted for in the case of provision of secondary members
5. The wind loads on the members are equally distributed to the connecting
joints.
Step3: Calculation of solidity ratios: Ref P.7 code
Solidity ratio for different panels are calculated
( ) Pr ojected area of all theindividualelementsSolidity ratioArea enclosed by the boundaryof theframe normal to the wind direction
φ =
Solidity ratios of panel 1 to 15 are calculated once as panels 1 to 15 are
similar
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
( ) ( )1 15
1 15 16
1 16
16
17
17
18
15x 2 2 x 0.15 15x 2 2 x 2 x 0.05 16 x 2 x 0.045
30 x 20.245 Similarly for
2 x 4.04 x 0.15 2 x 4.68x 0.065 2.8x 0.052 2.8 x 4
20.204
2 x 4.04 x 0.15 2 x 5.14 x 0.065 1x 3.6 x 0.0652 3.6 x 4
20.165
2
−
−
−
+ +φ =
φ = φ
+ +φ =
+⎛ ⎞⎜ ⎟⎝ ⎠
φ =
+ +φ =
+⎛ ⎞⎜ ⎟⎝ ⎠
φ =
φ =
18
x 4.04 x 0.2 2 x 5.67 x 0.065 1x 4.4 x 0.0653.6 4.4 x 4
20.165
+ ++⎛ ⎞
⎜ ⎟⎝ ⎠
φ =
19
19
20
20
2 x 4.04 x 0.2 2 x 4.79 x 0.065 1x 5.2 x 0.0654.4 5.2 x 4
20.134
2 x 4.04 x 0.2 2 x5.016 x 0.0655.2 6 x 4
20.101
+ +φ =
+⎛ ⎞⎜ ⎟⎝ ⎠
φ =
+φ =
+⎛ ⎞⎜ ⎟⎝ ⎠
φ =
Step4 : Calculation of bowl wind pressure
Ref. Fig6 P.44 code. Bowl wind coeffs. are
cf = 1.4 for wind from front
cf = 0.4 for wind from rear
wind pressure at 50m above GL
Design wind pressure PZ =1476.6 (1.09)2
= 1.754 kN/m2
Wind loads on dish are on front face FDISH 1 = cf.Ae.pd
Ref. P.36 clause 6.3 code
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
FDISH 1 = 1.4 x π/4 x 22 x 1.754
= 7.71 kN
On rear face
FDISH 2 = 0.4 x π/4 x 22 x 1.754
= 2.20 kN
Step5:
The terrain factor (k2), the solidity ratio and the design wind pressures at
various heights are tabulated as shown - category 3 class B
Panel from top
Height in 'm' from top
Terrain size,HT. coeff. k2
Design wind pressure PZ=1476.6 (k2
2) N/m2
Solidity ratio
Overall force coeff. cfTable30 P.47
PZ . cf N/m2
1 to 5 10 1.09 = 1.075 1.06
1706.4 0.245 3.075 5247.2
6 to 10 20 1.06 = 1.045 1.03
1612.5 0.245 3.075 4958.4
11 to 15 30
1.03 = 1.005 0.98
1491.4 0.245 3.075 4586.1
16 34 0.98 = 0.964 0.948
1372.2 0.204 3.28 4500.8
17 38 0.948 = 0.926 0.904
1266.1 0.165 3.475 4399.7
18 42 0.904 = 0.88 0.856
1143.5 0.165 3.475 3975.7
19 46 0.856 = 0.832 0.808
1022.1 0.134 3.630 3710.2
20 50 0.808 964.0 0.101 3.795 3658.4
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Step6: Calculation of forces at different joints
The forces from the dish are transferred to two top most joints 1 and 4.
The dish weight and wind force on the dish are equally distributed at the two
joints.
Panel 1 Leg: Length of the leg = 2m
Width of the leg = 0.15m
Since 4 Nos of ISA 150 x 150 x 12 @ 0.272 kN/m
Self weight of legs = 4 x 2 x 0.272 = 2.176 kN
No. of legs exposed to wind = 2
Wind obstruction area = 2 x 2 x 0.15
= 0.6 m2
wind load on leg = 0.6 x 5247.2
= 3.148 kN
Diagonal bracing : No. of diagonal bracings = 8
No. of obstructing wind = 2
Size of diagonal bracing ISA 50 x 50 x 6 @ 0.045 kN/m.
Self weight = 8 x x 2 x 0.045
= 1.018 kN
Wind obstruction area = 2 x x 2 x 0.05
= 0.283 m2
Wind load on diag. Brac = 0.283 x 5247.2
= 1.485 kN
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Horizontal bracing: ISA 45 x 45 x 6
No. of horizontal bracings = 8
No. of obstructing wind = 2
Self weight of horizontal bracing = 8 x 2 x 0.04
= 0.64 kN
Wind obstruction area = 2 x 2 x 0.045
= 0.18m2
Wind load on horizontal brac = 0.18 x 5247.2
= 0.945 kN
Total self weight of leg, diag. brac and horizontal brac
Fv = 2.176 + 1.018 + 0.64 = 3.834 kN
Total wind load on leg, diag and Hor. bracs
FH = 3.148 + 1.485 + 0.945 = 5.578 kN
These load are to be distributed to all the 8 joints connecting the elements (i.e.
joints 1 to 8)
Load at each joint is increased by 15% to account for gussets, bolts and
washers
Fv1 vertical load on joints 1 to 8 = 1.15 x 3.834 / 8
= 0.551 kN
FH1 wind load on joints 1 to 8 = 1.15 x 5.576 / 8
= 0.802 kN
The self weight of the dish is shared by joints 1 and 4
FV DISH = 10/2 kN = 5kN
Wind load on the dish is shared by joints 1, 2, 3 and 4, FH DISH = 7.71 / 4 =
1.93 kN
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Panel 2: Self weight of legs = 2.176 kN
wind load on legs = 3.148 kN
Self weight of diag. Bracs = 1.018 kN
Wind load on Diag. Brac = 1.485 kN
No. of horizontal bracings = 4
No. of obstructing wind = 4
Self weight of horizontal bracing = 4 x 2 x 0.04
= 0.32 kN
Wind obstruction area = 1 x 2 x 0.045
= 0.09 m2
Wind load on hor. brac. = 0.09 x 5247.2 = 472.2 N
Vertical load due to leg and diag. brac carried by joints 5 to 12 = 1.15 (2.176 +
1.018) / 8
= 0.46 kN
Vertical load due to hor.brac. carried by joints 9, 10, 11 and 12 = 1.15 x
(0.32)/4 = 0.092 kN
Wind load carried by joints 5 to 12 = 1.15 (3.148 + 1.485) / 8
= 0.666 kN
Wind load carried by joints 9, 10, 11 and 12 = 1.15 x 0.472/4
= 0.136 kN
Computation of loads at different joints are made for panel to panel from panel
2 to panel 5 are tabulated
Panel 6: Self weight of legs = 4 x 2 x 0.272 = 2.176 kN
Wind load = 0.6 x 4958.4 = 2.975 kN
Self weight of Diag. Brac. = 1.018 kN
Wind load = 0.283 x 4958.4 = 1.403 kN
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Self weight of hor. bracings = 0.32 kN
Wind load = 0.09 x 4958.4 = 0.446 kN
Vertical load carried by joints 21 to 28 = (2.176 + 1.018) 1.15 / 8
= 0.46 kN
Wind load carried by joints 21 to 28 = (2.975 + 1.403) 1.15 / 8
= 0.63 kN
Vertical load due to Hor. Brac. carried by joints 25, 26, 27 and 28 = 1.15 x
(0.32)/4
= 0.092 kN
Wind load carried by joints 25, 26, 27 and 28 = 1.15 x (0.446)/4
= 0.128 kN
Computations of loads at different joints were done from 6 to 10 and are
tabulated.
Panel 11: Vertical load carried by joints 41 to 48 = 0.46 kN
Wind load on the legs = 0.6 x 4586.1
= 2.75 kN
Wind load on the Diag. Brac. = 0.283 x 4586.1
= 1.3 kN
Vertical load due to Hor. Brac carried by joints 45, 46, 47 and 48 = 0.092 kN
Wind load carried by joints 41 to 48 = 1.15 (2.75 + 1.3)/8
= 0.582 kN
Wind load carried by joints 45 to 48 due to Hor. Brac. = (0.09 x 4586.1)/4
Computation of loads at different joints were done from panel 11 to 15 and are
tabulated
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Panel 16: Leg: ISA 150 x 150 x 15 @ 0.336 kN/m
Length of the leg (L) = 4.04m
Width of the leg (B) = 0.15m
Self weight of legs = 4 x 4.04 x 0.336
= 5.43 kN
No. of legs exposed to wind = 2
Wind obstruction area = 2 x 4.04 x 0.15
= 1.212 m2
Wind load on leg = 1.212 x 4500.8
= 5.454 kN
Diag. Brac: ISA 65 x 65 x 5 @ 0.049 kN/m
No. of bracing = 8
No. of obstructing wind = 2
Self weight of diagonal brac. = 8 x 4.68 x 0.049
= 1.835 kN
Wind obstruction area = 2 x 4.68 x 0.065
= 0.6084 m2
Wind load on Diag. Brac = 0.6084 x 4500.8
= 2.74 kN
Horizontal Brac: ISA 65 x 65 x 5 @ 0.045 kN/m
No. of bracing = 4
No. of obstructing wind = 1
Self weight of Hor. brac. = 4 x 2.8 x 0.045
= 0.504 kN
Wind obstruction area = 1 x 2.8 x 0.050
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
= 0.14 kN
Wind load on Hor. Brac = 0.14 x 4500.8
= 0.63 kN
Secondary bracings are accounted for so DL and WL is increased by 10%
Vertical load carried by joints 61 to 68 = (1.25 / 5.43 + 1.835)/8
= 1.135 kN
Vertical load carried by joints 65 to 68 due to Hor. Brac. = 1.25 (0.504)/4
= 0.158 kN
Wind load carried by joints 61 to 68 = 1.25 (5.454 + 2.74)/8
= 1.28 kN
Wind load carried by joints 65 to 68 due to Hor. Brac = 1.25 (0.63) / 4
= 0.197 kN
Panel 17: Leg: ISA 150 x 150 x 16 @ 0.336 kN/m
Self weight of legs = 4 x 4.04 x 0.336
= 5.43 kN
Wind obstruction area = 2 x 4.04 x 0.15
= 1.212 m2
Wind load on leg = 1.212 x 4399.7
= 5.332 kN
Diag. Brac: ISA 65 x 65 x 5 @ 0.049 kN/m
Self weight of diagonal brac. = 8 x 5.14 x 0.049
= 2.015 kN
Wind obstruction area = 2 x 5.14 x 0.065
= 0.6682 m2
Wind load on Diag. Brac = 0.6682 x 4399.7
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
= 2.94 kN
Horizontal Brac: ISA 65 x 65 x 6 @ 0.058 kN/m
Self weight of Hor. brac. = 4 x 3.6 x 0.058
= 0.835 kN
Wind obstruction area = 1 x 3.6 x 0.065
= 0.234 m2
Wind load on Hor. Brac = 0.234 x 4399.7
= 1.03 kN
Secondary bracings should be accounted for in this panel
Vertical load carried by joints 69 to 72 = 1.25 (5.43 + 2.015)/8
= 1.163 kN
Vertical load carried by (Due to horizontal brac.) joints 69 to 72 = 1.25
(0.835)/4
= 0.261 kN
Wind load carried by joints 65 to 72 = 1.25 (5.332 + 2.94)/8
= 1.29 kN
Wind load carried by joints 69 to 72 due to Hor. Brac = 1.25 (1.03) / 4
= 0.332 kN
Panel 18 : Leg: ISA 200 x 200 x 15 @ 0.454 kN/m
Self weight of legs = 4 x 4.04 x 0.454
= 7.34 kN
Wind obstruction area = 2 x 4.04 x 0.2
= 1.616 m2
Wind load on leg = 1.616 x 3973.7
= 6.42 kN
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Diag. Brac: ISA 65 x 65 x 6 @ 0.058 kN/m
Self weight of diagonal brac. = 8 x 5.67 x 0.058
= 2.63 kN
Wind load on Diag. Brac = 2 x 5.67 x 0.065 x 3973.7
= 2.93 kN
Horizontal Brac: ISA 65 x 65 x 6 @ 0.058 kN/m
Self weight of Hor. brac. = 4 x 4.4 x 0.058
= 1.02 kN
Wind load on Hor. Brac = 1 x 4.4 x 0.065 x 3973.7
= 1.14 kN
Vertical load carried by joints 69 to 79 except 74, 76, 78, 80 = 1.25 (7.34 +
2.68)/8
= 1.56 kN
Vertical load carried by joints 73, 75, 77, 79 (Due to horizontal brac.) = 1.25
(1.02)/4
= 0.32 kN
Wind load carried by joints 65 to 79 except 74, 76, 78, 80 = 1.25 (6.42 +
2.93)/8
= 1.46 kN
Wind load carried by joints 73, 75, 77, 79 due to Hor. Brac = 1.25 (1.14) / 4
= 0.356 kN
Panel 19: Leg: ISA 200 x 200 x 15 @ 0.454 kN/m
Self weight of legs = 4 x 4.04 x 0.454
= 7.34 kN
Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Indian Institute of Technology Madras
Wind load on leg = 2 x 4.04 x 0.2 x 3710.2
= 6 kN
Diag. Brac: ISA 65 x 65 x 6 @ 0.058 kN/m
Self weight of diagonal brac. = 8 x 4.79 x 0.058
= 2.22 kN
Wind load on Diag. Brac = 2 x 4.79 x 0.065 x 3710.2
= 2.31 kN
Horizontal Brac: ISA 65 x 65 x 6 @ 0.058 kN/m
Self weight of Hor. brac. = 4 x 5.2 x 0.058
= 1.21 kN
Wind load on Hor. Brac = 1 x 5.2 x 0.065 x 3710.2
= 1.254 kN
Vertical load carried by joints 73 to 88 except 74, 76, 78, 80, 82, 84, 86, 88 =
1.25 (7.34 + 2.22)/8
= 1.494 kN
Vertical load carried by joints 81, 83, 85, 87 (Due to horizontal brac.) = 1.25